I think there's gonna be alot of teenage pranks and destruction. People setting the landing spot in the water or people stealing them with nets. Not sure if much recourse unless there camera footage or gps locator.
This is the standard fear response to new technologies. Uber: how can you get in a car with a stranger? Airbnb: Even Paul Graham said "are you nuts?". Self driving cars: but what if people take advantage of it's collision avoidance abilities to walk in front? etc. etc. The fact is, most people are not malicious, life goes on anyway, and the risk of vandalism is quantifiable and included in the cost of doing business.
And in this case vandals can easily be prosecuted, since a drone is already hooked up with remote control, GPS tracking, cameras and monitoring.
I find a lot of the whole drone delivery thing pretty silly outside of some specific scenarios. Nonetheless, there is an equally silly "we must guarantee 100% reliability and security" thought." UPS does fine. They have no trouble leaving most packages at my door. They probably don't live the same thing at other doors. (Though I don't know their heuristics for such things.)
OTOH, I feel like if people today proposed that trucks leave unattended packages outside people's door, it would be dismissed as unworkable. But it happens constantly with minimal problems. There aren't as many bad people in the world as some people think.
The drones are almost certainly going to have cameras (for object avoidance) and GPS on-board in order to satisfy regulators that Amazon knows where its drones are and that they're safe. Consider Amazon's own airspace proposals linked in the FAQ of the article.
I think someone previously made the analogy of a lot of UPS trucks getting stolen. It could happen, but prosecution is probably a sufficient penalty to prevent it from being a serious issue.